Compatible Relatively dual weakly complemented lattice

The concept of relatively dual weakly complementation on a bounded lattice is introduced. Also, relatively dual weakly complemented (RDWC) and compatible RDWC lattices are defined. Some of the algebraic properties are investigated. Relative closed and dense sets of elements are defined and studied. Finally, some types of filters are defined on a compatible RDWC lattice, and the conditional relationships between different types of filters are investigated.